A subgradient-based branch-and-bound algorithm for the ...
A subgradient-based branch-and-bound algorithm for the ... A subgradient-based branch-and-bound algorithm for the ...
Table C.2 Detailed results on instances with ratio r = 10 no. BB-SG CPLEX UB nodes depth time gap UB nodes time gap |I| × |J| = 300 × 300 1 28474.02 293 13 16.18 28474.02 16422 2129.03 2 27008.17 527 14 53.10 27008.17 4302 1889.55 3 28826.24 1179 16 76.62 28826.24 23969 1465.70 4 27662.75 641 19 35.41 27662.75 9628 679.58 5 28682.42 917 18 51.89 28682.42 5395 874.07 |I| × |J| = 500 × 500 1 45081.83 3921 22 455.12 45081.83 45037 20855.99 2 43420.27 273 17 33.40 43420.27 24829 12012.48 3 44899.66 23257 28 3458.19 44968.09 73300 44505.23 0.40 a 4 43396.79 22153 23 2794.76 43438.93 52200 48614.37 0.27 a 5 43511.99 1129 23 93.76 43511.99 11031 2328.70 |I| × |J| = 700 × 700 1 59572.55 71615 30 14022.36 59572.55 95800 40789.26 0.08 a 2 60832.31 44023 23 7468.60 60846.78 60000 56448.26 0.13 a 3 62120.52 237975 30 100000.42 0.03 b 62249.18 83400 37008.56 0.37 a 4 60055.82 95551 31 20122.04 60101.53 64700 72927.47 0.19 a 5 60920.86 167490 84648.77 0.04 a 61139.75 62400 30543.04 0.58 a |I| × |J| = 1000 × 1000 1 85384.46 47515 22 100000.02 0.10 b 85549.72 61000 64249.75 0.40 a 2 83054.52 64427 23 100002.41 0.11 b 83394.50 54600 41384.11 0.61 a 3 82864.38 59797 27 25859.98 82933.14 57500 47629.46 0.16 a 4 84331.57 80936 73527.65 0.06 a 84506.92 48600 32129.46 0.36 a 5 83394.66 56473 33 18786.89 83394.66 42800 66488.31 0.07 a |I| × |J| = 1500 × 300 1 49730.88 20261 30 4433.79 2 50255.27 7581 19 3458.74 3 49974.14 8605 22 1970.75 4 49869.27 5233 24 1466.44 5 50925.93 5877 23 1938.76 |I| × |J| = 1500 × 600 1 65859.94 152305 34 68850.16 2 63493.10 36909 27 13032.79 3 67117.28 61290 57054.54 0.07 a 4 65277.42 60512 73016.79 0.14 a 5 65151.72 61718 51813.71 0.07 a a Terminated due to insufficient memory. b Time limit of 100,000 seconds reached. 30
Table C.3 Detailed results on instances with ratio r = 15 no. BB-SG CPLEX UB nodes depth time gap UB nodes time gap |I| × |J| = 300 × 300 1 21253.35 13 5 1.63 21253.35 53 79.32 2 21814.36 73 8 4.74 21814.36 820 1 45.76 3 22529.39 1941 17 130.95 22529.39 16858 5382.56 4 22168.57 91 9 3.91 22168.57 744 154.62 5 22523.41 917 17 44.26 22523.41 13522 2890.04 |I| × |J| = 500 × 500 1 33435.69 1019 21 123.56 33435.69 18186 19391.52 2 33507.69 329 13 44.14 33507.69 6890 3722.35 3 33959.00 2277 15 497.95 33959.00 20300 30996.04 0.16 c 4 33709.19 15603 20 1576.54 33785.23 68400 32433.31 0.42 a 5 33833.95 6947 23 823.59 34025.29 69100 29448.15 0.81 a |I| × |J| = 700 × 700 1 45104.89 5183 24 1147.89 45104.89 43385 61078.82 2 45100.44 59121 30 8749.40 45101.74 56500 73651.92 0.17 a 3 45032.72 34687 26 5503.07 45100.81 51000 60907.68 0.28 a 4 44992.00 4219 16 852.30 44992.00 75694 100425.30 0.04 b 5 46197.17 22581 21 6428.29 46451.16 44900 39507.25 0.74 a |I| × |J| = 1000 × 1000 1 62522.86 71933 30 100000.17 0.14b 62605.11 33300 77854.68 0.43a 2 62492.39 75877 23 100001.02 0.08b 62796.25 31700 44235.52 0.75a 3 62025.59 149679 31 56430.57 62186.92 39700 61674.28 0.46a 4 62404.53 105551 31 43359.93 62471.88 32900 72169.08 0.23a 5 62401.91 218013 100000.04 0.02b 62768.69 28400 49560.19 0.81a 1 46379.99 1007 18 |I| × |J| = 1500 × 300 391.25 2 45562.90 13541 22 2995.91 3 45872.96 1181 17 497.83 4 46456.43 441 14 199.65 5 46516.67 259 17 138.23 |I| × |J| = 1500 × 600 1 54285.13 82527 41 26848.46 2 54459.33 2995 16 1341.99 3 54273.96 14707 23 4902.58 4 54688.17 18575 23 6923.03 5 54626.06 13159 25 5939.51 a Terminated due to insufficient memory. b Time limit of 100,000 seconds reached. c CPLEX terminated with a segmentation fault. 31
- Page 1: DEPARTMENT OF OPERATIONS RESEARCH U
- Page 4 and 5: customer i’s demand from facility
- Page 6 and 7: otherwise a “null step” is perf
- Page 8 and 9: global upper bound computed so far,
- Page 10 and 11: Table 1 Comparison of B&P and BB-SG
- Page 12 and 13: Table 3 Comparison of CAPLOC and BB
- Page 14 and 15: Table 6 Comparison of CPLEX and BB-
- Page 16 and 17: Table 9 Comparison of CPLEX, B&C an
- Page 18 and 19: Table 11 Comparison of CPLEX and BB
- Page 20 and 21: Table 12 Comparison of BB-SG and BB
- Page 22 and 23: position method for two stage stoch
- Page 24 and 25: Table A.2 Detailed results on insta
- Page 26 and 27: B Detailed results obtained with BB
- Page 28 and 29: Table B.3 Detailed results on insta
- Page 30 and 31: C Detailed results obtained with BB
- Page 34 and 35: Table C.4 Detailed results on insta
- Page 36 and 37: *----------------------------------
- Page 38 and 39: } } d = ( int *) calloc (m, sizeof
- Page 40: libs = -lm $( main ): $( obj ) $( L
Table C.3<br />
Detailed results on instances with ratio r = 15<br />
no. BB-SG CPLEX<br />
UB nodes depth time gap UB nodes time gap<br />
|I| × |J| = 300 × 300<br />
1 21253.35 13 5 1.63 21253.35 53 79.32<br />
2 21814.36 73 8 4.74 21814.36 820 1 45.76<br />
3 22529.39 1941 17 130.95 22529.39 16858 5382.56<br />
4 22168.57 91 9 3.91 22168.57 744 154.62<br />
5 22523.41 917 17 44.26 22523.41 13522 2890.04<br />
|I| × |J| = 500 × 500<br />
1 33435.69 1019 21 123.56 33435.69 18186 19391.52<br />
2 33507.69 329 13 44.14 33507.69 6890 3722.35<br />
3 33959.00 2277 15 497.95 33959.00 20300 30996.04 0.16 c<br />
4 33709.19 15603 20 1576.54 33785.23 68400 32433.31 0.42 a<br />
5 33833.95 6947 23 823.59 34025.29 69100 29448.15 0.81 a<br />
|I| × |J| = 700 × 700<br />
1 45104.89 5183 24 1147.89 45104.89 43385 61078.82<br />
2 45100.44 59121 30 8749.40 45101.74 56500 73651.92 0.17 a<br />
3 45032.72 34687 26 5503.07 45100.81 51000 60907.68 0.28 a<br />
4 44992.00 4219 16 852.30 44992.00 75694 100425.30 0.04 b<br />
5 46197.17 22581 21 6428.29 46451.16 44900 39507.25 0.74 a<br />
|I| × |J| = 1000 × 1000<br />
1 62522.86 71933 30 100000.17 0.14b 62605.11 33300 77854.68 0.43a 2 62492.39 75877 23 100001.02 0.08b 62796.25 31700 44235.52 0.75a 3 62025.59 149679 31 56430.57 62186.92 39700 61674.28 0.46a 4 62404.53 105551 31 43359.93 62471.88 32900 72169.08 0.23a 5 62401.91 218013 100000.04 0.02b 62768.69 28400 49560.19 0.81a 1 46379.99 1007 18<br />
|I| × |J| = 1500 × 300<br />
391.25<br />
2 45562.90 13541 22 2995.91<br />
3 45872.96 1181 17 497.83<br />
4 46456.43 441 14 199.65<br />
5 46516.67 259 17 138.23<br />
|I| × |J| = 1500 × 600<br />
1 54285.13 82527 41 26848.46<br />
2 54459.33 2995 16 1341.99<br />
3 54273.96 14707 23 4902.58<br />
4 54688.17 18575 23 6923.03<br />
5 54626.06 13159 25 5939.51<br />
a Terminated due to insufficient memory.<br />
b Time limit of 100,000 seconds reached.<br />
c CPLEX terminated with a segmentation fault.<br />
31
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